Fractions Chapter Notes | Year 4 Mathematics IGCSE (Cambridge) - Class 4 PDF Download

Understanding fractions

• The objective is to demonstrate that dividing a whole into more equal parts results in smaller fractions.
• A fraction can be represented as a division of the numerator by the denominator.
• Fractions are written with a numerator and a denominator, e.g., 3/4 is read as ‘three-quarters’.
• When dividing a shape into fractions, the shape must be divided into equal parts.
• Each part must be the same size, though parts can be positioned differently.
• The more parts a whole is divided into, the smaller each fraction becomes, e.g., 1/5 < 1/4 < 1/3 < 1/2.
• A fraction like 3/4 represents 3 ÷ 4.
• For example, dividing a hexagon into four equal parts results in quarters, expressed as 1 ÷ 4 = 1/4.

Fractions as operators

• A unit fraction is defined as a fraction with a numerator of 1, e.g., 1/5.
• Unit fractions can be used as operators to find a fraction of a quantity.
• To find one-fifth of a quantity, divide by 5, e.g., 1/5 of 30 = 30 ÷ 5 = 6.
• To find one-sixth of a quantity, divide by 6, e.g., 1/6 of 24 = 24 ÷ 6 = 4.
• In practical applications, such as cooking, halving a recipe involves finding fractions of ingredient amounts, e.g., 1/2 of 350 = 175, so 175 g of flour is needed.
• When sharing quantities equally, fractions are used, e.g., 1/4 of 3 = 3 ÷ 4 = 3/4, meaning each person gets 3/4 of a chocolate bar when 3 bars are shared among 4 people.